Problem: Simplify the following expression: $ k = \dfrac{-5x}{3x - 6} - \dfrac{-1}{6} $
In order to subtract expressions, they must have a common denominator. Multiply the first expression by $\dfrac{6}{6}$ $ \dfrac{-5x}{3x - 6} \times \dfrac{6}{6} = \dfrac{-30x}{18x - 36} $ Multiply the second expression by $\dfrac{3x - 6}{3x - 6}$ $ \dfrac{-1}{6} \times \dfrac{3x - 6}{3x - 6} = \dfrac{-3x + 6}{18x - 36} $ Therefore $ k = \dfrac{-30x}{18x - 36} - \dfrac{-3x + 6}{18x - 36} $ Now the expressions have the same denominator we can simply subtract the numerators: $k = \dfrac{-30x - (-3x + 6) }{18x - 36} $ Distribute the negative sign: $k = \dfrac{-30x + 3x - 6}{18x - 36}$ $k = \dfrac{-27x - 6}{18x - 36}$ Simplify the expression by dividing the numerator and denominator by 3: $k = \dfrac{-9x - 2}{6x - 12}$